A paucity of bulk entangling surfaces: AdS wormholes with de Sitter interiors

TL;DR

This paper constructs specific AdS-dS wormhole spacetimes with two asymptotic AdS boundaries and finds that the usual bulk entangling surfaces used for entropy calculations do not exist, challenging the applicability of the HRT prescription.

Contribution

It introduces planar AdS-dS wormholes with null energy condition compliance where standard HRT entangling surfaces are absent, indicating the need for modified entropy computation methods.

Findings

No real codimension-2 extremal surface connects the two boundaries.

Mutual information between finite subregions vanishes at leading order.

HRT entropy may be ill-defined for these wormholes, requiring new prescriptions.

Abstract

We study and construct spacetimes, dubbed planar AdS-dS-wormholes, satisfying the null energy condition and having two asymptotically AdS boundaries connected through a (non-traversable) inflating wormhole. As for other wormholes, it is natural to expect dual descriptions in terms of two disconnected CFTs in appropriate entangled states. But for our cases certain expected bulk entangling surfaces used by the Hubeny-Rangamani-Takayanagi (HRT) prescription to compute CFT entropy do not exist. In particular, no real codimension-2 extremal surface can run from one end of the wormhole to the other. According to HRT, the mutual information between any two finite-sized subregions (one in each CFT) must then vanish at leading order in large $N$ -- though the leading-order mutual information per unit area between the two CFTs taken as wholes may be nonzero. Some planar AdS-dS-wormholes also fail to have plane-symmetric surfaces that would compute the total entropy of either CFT. We suggest this to remain true of less-symmetric surfaces so that the HRT entropy is ill-defined and some modified prescription is required. It may be possible to simply extend HRT or the closely-related maximin construction by a limiting procedure, though complex extremal surfaces could also play an important role.